Variable neighbourhood search algorithms for asymmetric travelling salesman problems

The aim of the research is to find the best neighbourhood structures for the shaking step and the local search step in the variable neighbourhood search algorithm (VNS) when applied to the asymmetric travelling salesman problem (ATSP). Many variants of the VNS algorithm are proposed based on their neighbourhood structures. The performances of these VNS algorithms are tested with the benchmark instances of the ATSP, one of the best known logistics problems.